Robert M. Gary writes:

As I was watching the special and they described how the captain
reacted to the stall warning I couldn't help wonder if he attended the
same tailplane icing course I did. His reaction was text book correct
for a tailplane stall in icing conditions (pull back, not push
forward). He may have believed his problem was ice, not an typical
stall scenario.

The evidence for his overall incompetence was strong enough that it is
unlikely he'd have specific competence in dealing with tailplane icing. It's
more likely that he was responding instinctively--and incorrectly--to the
circumstances.

Tailplane icing was indeed considered as a possibility initially, before the
long list of errors made by the pilots became fully apparent.